Topological Insulators, Chern Insulators, and Topological Charge Density Waves*

We present a theory on the quantum phase diagram of AB-stacked MoTe₂/WSe₂ using a self-consistent Hartree-Fock calculation performed in the plane-wave basis without projection to a lattice model, motivated by the observation of topological states in this system. At filling factor ν=2 (two holes per moiré unit cell), Coulomb interaction stabilizes a Z₂ topological insulator by opening a charge gap. At ν=1, the interaction induces two competing states, a spin density wave Mott insulator and a valley polarized state, which could undergo a first-order phase transition tuned by an out-of-plane displacement field. The valley polarized state becomes a Chern insulator for certain displacement fields.  Moreover, we predict a topological charge density wave forming a honeycomb lattice with ferromagnetism at ν=2/3. Possible future directions on this type of moiré bilayers hosting a rich set of quantum phases are discussed.